For years, Western intelligence services have focused on taking down al Qaeda in the tribal areas of Pakistan. They have done so with great success, killing Osama bin Laden and eliminating other top leadership.

But al Qaeda is far from finished. In Yemen, it is thriving and its local affiliate, al Qaeda in the Arabian Peninsula (AQAP), has emerged as the group’s most dangerous franchise. Last week’s underwear bomb plot—foiled by the CIA and allied agencies—is but the latest example.

Unlike other al Qaeda affiliates, AQAP can count on many experienced operators. It has a strong and growing local power base, and it is relentless in its determination to attack America.

It is from Yemen, not the tribal areas of Pakistan, that al Qaeda is most likely to strike America next. Western security services are right, therefore, to keep shifting resources and attention to fighting AQAP.

According to the FBI, the bomb that AQAP wanted to use in last week’s plot is a more sophisticated version of the original underwear bomb that failed to explode over Detroit on Christmas Day in 2009. It was constructed by Ibrahim Hassan Asiri, a Saudi bomb-maker who has pioneered the use of Nitropenta, a plastic explosive that is hard to detect even with the most advanced security equipment. Top of the CIA’s target list, al-Asiri has spent the past few months passing on his knowledge to others.

But AQAP’s talent pool is not limited to al Asiri. At its core are 100 veteran jihadists, who escaped local prisons in 2006 and 2011. The group also counts on 11 former Guantanamo detainees, who returned to terrorism after undergoing “rehabilitation” programs in Saudi Arabia.

Their combined experience is greater than that of all other al Qaeda affiliates taken together. In Yemen, AQAP’s insurgency against the central government is increasingly successful. As early as 2010, insurgency expert Ryan Evans was warning in West Point’s CTC Sentinel that AQAP “genuinely adopts the grievances and interests of Yemenis.” Moreover, “Its attacks are smaller [than those of other al Qaeda affiliates], and the group does not target Yemeni civilians.”

Unlike al Qaeda in Iraq, which alienated entire tribes with barbaric and indiscriminate violence, AQAP’s policies have allowed it to cultivate local sympathies. In the central region surrounding Sana’a, the group has forged alliances with some of Yemen’s most influential tribes. Though reports are conflicting, it now appears to hold several towns and controls territory in three provinces. Immersed in the population and protected by the tribes, AQAP is free to raise money and train fighters. CIA drone strikes against its operatives, in turn, are more likely to kill civilians.

What makes AQAP unique among al Qaeda affiliates is the amount of energy and resources it devotes to attacking America. The group’s foreign-operations wing has been responsible for much of al Qaeda’s propaganda aimed at Western Muslims. Its former leader, American born cleric Anwar al-Awlaki, was hugely popular and influential among jihadist sympathizers in the U.S. and Europe. One of al-Awlaki’s lieutenants, Samir Khan, produced the group’s English-language magazine Inspire, which has instructed readers on how to “build a bomb in the kitchen of your mom.”

Over the past three years, AQAP has sanctioned, inspired or planned at least half a dozen attacks against Western targets. Some were carried out by lone wolves who took their cues from the Internet and did not rely on the group’s organization or resources. Others, however, were centrally organized, which underlines the diversity of the threat.

For AQAP, even failures count as success. Its first underwear bomber in 2009 forced airports to buy expensive (and controversial) body scanners. The attempt to blow up packages on cargo planes in October 2010 nearly paralyzed international business. AQAP calls it “the strategy of a thousand cuts.” Unable to pull off another 9/11, “the aim is to bleed the enemy to death.”

But AQAP has weaknesses too. A Saudi agent’s successful infiltration of an AQAP cell, which resulted in the disruption of last week’s plot, will have shocked the group’s leadership and may cause internal ruptures. CIA drone strikes have killed al-Awlaki and his immediate successor, Fahd al-Quoso, leaving the group’s foreign-operations wing without a leader.

No doubt, such efforts must be sustained. For the foreseeable future, AQAP will remain the group’s most ambitious affiliate—and the one that is most determined to strike against the West.

Mr. Meleagrou-Hitchens is a research fellow at the International Centre for the Study of Radicalisation at King’s College in London. Dr. Neumann is a professor of security studies at King’s College in London.